The solution of the differential equation 2x dy dx - y = 3 represents a family of

Step-by-step solution

The given differential equation is 2x dy dx - y = 3 Rearranging the terms, we get: 2x dy dx = y + 3 Separating the variables: dy y + 3 = dx 2x Integrating both sides: dy y + 3 = dx 2x (y + 3) = 1 2 x + c (y + 3) = (c x ) y + 3 = c x Squaring both sides, we get: (y + 3)^2 = c^2 x This is an equation of the form Y^2 = 4aX , which represents a family of parabolas. Answer: parabola